1, according to the actual situation to determine the teaching difficulties:

In general, all the teaching knowledge points that need to be mastered through the transformation of teaching cognitive structure in learning are teaching difficulties. All the teaching knowledge points mastered by processing new knowledge through cognitive structure are not necessarily teaching difficulties. However, in practice, it needs to be flexibly positioned according to the actual level of students. In the same learning process, in the same kind of "teaching difficulties", different students in different classes are not necessarily difficult because of the differences in students' teaching cognitive structure and individual differences in the speed of encountering difficulties or breaking through difficulties. For example, division, fraction and ratio are three related and different concepts. Through the transmission of knowledge, it not only helps students to master new knowledge, but also helps students to understand the similarities and differences between several concepts: although the former term of "Bi" is equivalent to divisor and numerator in division, the latter term is equivalent to denominator in division, and ":"is equivalent to divisor and fractional line in division, which can express the division relationship between two numbers, but division is an operation and fraction is a number. According to the relationship between the three, when solving these three types of application problems, students' ability to solve application problems can be improved through flexible conversion. For example, in teaching, a pesticide is mixed with water in a ratio of 1:2500. How many kilograms of this pesticide should be put in 1000 kilograms of water? It is one of the teaching difficulties of this course to answer these three concepts by three methods: ratio, fraction and division. In teaching, we must answer from different angles, communicate the relationship between these three types of application problems in different ways, break the mindset and improve students' ability to solve application problems.

2. Distinguish between teaching emphases and teaching difficulties.

The focus of teaching is "the premise rebellion that occupies a relatively important position in the specific level of the logical structure of teaching materials", that is, "the content that plays an important role in the whole knowledge system or discipline system". If a knowledge point is the core of a knowledge unit or the cornerstone of subsequent learning or has a wide range of applications, it can be determined that it is the focus of teaching. The focus of mathematics teaching is based on the internal logical structure of mathematical knowledge and exists objectively, so it is the same for every student.

However, the teaching difficulty is not. It is precisely because of the different bases for the formation of key points and difficulties that some contents are both important and difficult, some are important but not necessarily difficult, some are difficult but not necessarily important, and some are difficult but not necessarily equal to the difficulty of teaching. In the process of perceiving information related to problems, students are confused by old knowledge and experience, and unconsciously use previously familiar knowledge rules to solve new mathematical problems. Lead thinking activities astray. For example, some students are disturbed by the knowledge of understanding ratio (3: x = 6: 7) before solving equations. In the process of solving, he took X as the divisor of the equation and solved it by dividing the divisor by the dividend (x = 3 ÷). For example, when learning simplification, students can easily confuse simplification with comparison, like the simplification ratio of 4: =.

In short, the interference of this kind of knowledge will often make students confused when learning new knowledge and make mistakes when choosing the wrong knowledge when solving problems. This is a difficult point in mathematics teaching.